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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 7: Q.AP2.21 - Cumulative AP Practise Test (page 438)

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest $80 %$ of calls will take how long to complete?
a. Less than 10 minutes
b. At least 10 minutes
c. Exactly 10 minutes
d. At least $5.5$ minutes
e. Less than $5.5$ minutes

Short Answer

Expert verified

a. Less than 10 minutes

Step by step solution

01

Given Information

02

Explanation for correct option

Finding $80 %$ on the $Y$ -axis, sketch a line to the right side until it touches the blue graph. Therefore it is cumulative; everything to the left side would be less than 10 minutes. The value will be 10 minutes therefore the shortest $80 %$ of the call would be less than 10 minutes.

Hence, the correct option is (a)

03

Explanation for incorrect option

b. At least 10 minutes is not the answer.

c. Exactly 10 minutes is not the answer.

d. At least 5.5 minutes is not the answer.

e. Less than 5.5 minutes is not the answer.

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Most popular questions from this chapter

Squirrels and their food supply ( $3.2$ ) Animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that sometimes has very large crops. Researchers collected data on an index of the abundance of pinecones and the average number of offspring per female over $16$ years. $4$ Computer output from a least-squares $4$ regression on these data and a residual plot are shown here

a. Is a linear model appropriate for these data? Explain.

b. Give the equation for the least-squares regression line. Define any variables you use.

c. Interpret the values of $r^{2}$ and $s$ in context.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

Bias and variability The figure shows approximate sampling distributions of $4$ different

statistics intended to estimate the same parameter.

a. Which statistics are unbiased estimators? Justify your answer.

b. Which statistic does the best job of estimating the parameter? Explain your answer.

Tall girls? To see if the claim made in Exercise $12$ is true at their high school, an Ap Statistics class chooses an SRS of twenty $16$ -year-old females at the school and measures their heights. In their sample, the mean height is $64.7$ inches. Does this provide convincing evidence that $16$ -year-old females at this school are taller than $64$ inches, on average?

a. What is the evidence that the average height of all $16$ -year-old females at this school is greater than $64$ inches, on average?

b. Provide two explanations for the evidence described in part (a).

We used technology to simulate choosing $250$ SRSs of size $n = 20$ from a population of three hundred $16$ -year-old females whose heights follow a Normal distribution with mean localid="1654113150676" $μ = 64$ inches and standard deviation $μ = 2.5$ inches. The dotplot shows $x =$ the sample mean height for each of the $250$ simulated samples.

c. There is one dot on the graph at $62.5$ . Explain what this value represents.

d. Would it be surprising to get a sample mean of $x = 64.7$ or larger in an SRS of size $20$ when $μ = 64$ inches and $σ = 2.5$ inches? Justify your answer.

e. Based on your previous answers, is there convincing evidence that the average height of all $16$ -year-old females at this school is greater than $64$ inches? Explain your reasoning.

Dem bones ( $2.2$ ) Osteoporosis is a condition in which the bones become brittle due to the loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in a standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is $2.5$ standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.

a. What percent of healthy young adults have osteoporosis by the WHO criterion?

b. Women aged $70$ to $79$ are, of course, not young adults. The mean BMD in this age group is about $- 2$ on the standard scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population has osteoporosis?

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